散布图

Correlation Does Not Mean Causation

Before we begin, here's a quick overview of everything related to correlation and causation.

$$\begin{align} &\circ\quad\small{\href{https://www.expii.com/t/scatter-plots-4393?type=explanation&id=7653}{\text{Scatter Plots}}}\\ &\circ\quad\small{\href{https://www.expii.com/t/scatter-plot-graph-correlation-4394?type=explanation&id=7667}{\text{Correlation}}}\\ &\circ\quad\small{\href{https://www.expii.com/t/trend-lines-graph-4395?type=explanation&id=7664}{\text{Trend Lines}}}\\ &\circ\quad\small{\href{https://www.expii.com/t/line-of-best-fit-equation-4396?type=explanation&id=7666}{\text{Line of Best Fit}}}\\ &\circ\quad\small{\href{https://www.expii.com/t/line-of-best-fit-equation-4396?type=explanation&id=7668}{\text{Interpolation and Extrapolation}}}\\ &\color{green}{\checkmark}\quad\small{\text{Causation}}\\ \end{align}$$

You might have heard this expression before, and it is a really important one. Just because two things have a correlation, it doesn't mean one causes the other to happen.

One of my favorite correlations is the number of movies Nic Cage is in each year and the number of drownings. They are positively correlated, meaning as Nic Cage makes more movies within a year, more people drown each year. But this doesn't mean that Nic Cage is the cause of these drownings, that's ridiculous. Sometimes in our chaotic world, things just line up like that.

To truly figure out if something causes something else, we need to do more test, more simulations, and more math!

(Video) This and That

by AsapSCIENCE

(Video) How Do You Use a Scatter Plot?

by eHow

Maria from eHow Education has a great, quick video that explains what a scatter plot is and when to use it.

$\large{\text{Summary}}$

A scatter plot is used to determine whether two variables have a correlation.

For example, in the video she looks to see if there's a correlation between the number of hours studied, and the grade received on a test.

Here's the axes of our graph.

Next, we plot our data.

Looking at these points we see there is a relationship. Not a direct correlation, though; there are other factors that play a part in the grade of your test. Just because people studied longer doesn't necessarily mean they get a higher grade. The person who studied for $3$ hours got a higher grade than the person who studied for $4$ hours.

But, on average, the people who studied longer, got higher grades. We call this a trend. We can eventually use a line of best fit to model the relation which we learn about later.

(Video) Scatter Diagrams

by HEGARTYMATHS

Here's a video by HEGARTYMATHS explaining scatter plots and different questions they can ask you about the diagrams.

$\large{\text{Summary}}$

A scatter plot is used to plot two variables against each other. There are three different types:

1. A positive correlation happens when, as your $x$ values increase, so do your $y$ values. Hour studying and test score could have a positive correlation.
2. A negative correlation happens when, as your $x$ values increase, your $y$ values decrease. Hours spent reading and pages left in your book could have a negative correlation.
3. No correlation happens when, as your $x$ values increase, your $y$ values show no trend. The number of wild turkeys in Pennsylvania and the hours you spend on your phone probably have no correlation.

Next, he goes over the different questions that could be asked of you on a test. They are:

1. Determine the relationship between the variables. This can be a positive correlation, a negative correlation, or no correlation.
2. Plot a point.
3. Draw a line of best fit.
4. Estimate a value using your line of best fit.

What is a Scatter Plot?

Before we begin, here's a quick overview of everything related to scatter plots.

$$\begin{align} &\color{green}{\checkmark}\quad\small{\text{Scatter Plots}}\\ &\circ\quad\small{\href{https://www.expii.com/t/scatter-plot-graph-correlation-4394?type=explanation&id=7667}{\text{Correlation}}}\\ &\circ\quad\small{\href{https://www.expii.com/t/trend-lines-graph-4395?type=explanation&id=7664}{\text{Trend Lines}}}\\ &\circ\quad\small{\href{https://www.expii.com/t/line-of-best-fit-equation-4396?type=explanation&id=7666}{\text{Line of Best Fit}}}\\ &\circ\quad\small{\href{https://www.expii.com/t/line-of-best-fit-equation-4396?type=explanation&id=7668}{\text{Interpolation and Extrapolation}}}\\ &\circ\quad\small{\href{https://www.expii.com/t/correlation-vs-causation-4397?type=explanation&id=7669}{\text{Causation}}}\\ \end{align}$$

A scatter plot is a bunch of points on a graph. Each point represents two sets of data.

For example, you can look at the number of glasses of water someone drinks in a day and the number of times someone goes to the bathroom in a day.

Each point on this graph could represent a different person. For example, the point $(3,1)$ could refer to Dante who drank $3$ glasses of water that day but only needed to use the bathroom once.

Why Use a Scatter Plot?

These plots are very useful for finding a relationship between two sets of data.

In the above example, you can see that on average, as a person drinks more water, they use the bathroom more.

We say on average because it's not always the case. There are other factors that determine whether or not you use the bathroom besides just the amount of water you drink.

Take a look at the points $(2,4)$ and $(6,1)$. Let's say these represent Charles, who drank $2$ glasses of water and needed to use the bathroom $4$ times, and Gina, who drank $6$ glasses of water and only needed to use the bathroom once.

Notice that just because Gina drank more water than Charles, it doesn't mean she uses the bathroom more. Maybe Charles has a weak bladder, maybe Gina has a stronger bladder. Maybe Charles has a really nice bathroom and likes using it. Maybe Gina used smaller glasses of water than Charles did.

Looking at the points as a collection, though, we do see higher bathroom uses from higher glasses consumed.

Correlations

Before we begin, here's a quick overview of everything related to correlations.

$$\begin{align} &\circ\quad\small{\href{https://www.expii.com/t/scatter-plots-4393?type=explanation&id=7653}{\text{Scatter Plots}}}\\ &\color{green}{\checkmark}\quad\small{\text{Correlation}}\\ &\circ\quad\small{\href{https://www.expii.com/t/trend-lines-graph-4395?type=explanation&id=7664}{\text{Trend Lines}}}\\ &\circ\quad\small{\href{https://www.expii.com/t/line-of-best-fit-equation-4396?type=explanation&id=7666}{\text{Line of Best Fit}}}\\ &\circ\quad\small{\href{https://www.expii.com/t/line-of-best-fit-equation-4396?type=explanation&id=7668}{\text{Interpolation and Extrapolation}}}\\ &\circ\quad\small{\href{https://www.expii.com/t/correlation-vs-causation-4397?type=explanation&id=7669}{\text{Causation}}}\\ \end{align}$$

Correlations are connections/relationships between two things.

There are three main types of correlations we can see in scatter plots: positive correlations, negative correlations, and no correlation.

A positive correlation means that as the $x$ variable increases, so does the $y$ variable. Our example of glasses of water consumed vs. bathroom trips is a positive correlation. As glasses of water increases, bathroom trips also begins to increase. We can also tell by the upward sloping shape of the data.

A negative correlation means that as the $x$ variable increases, the $y$ variable decreases. They will have a downward sloping shape to the data. An example of this might be hours spent studying and problems missed on a test.

On average, those that studied more missed less problems.

Finally, no correlation is when the variables have no connection to each other. An example of this could be the number of times someone searches "rice" on Google, and the number of hats they own.

Here, there is no correlation. Googling rice more times doesn't lead to more hats owned or less hats owned.

Correlations can also be perfect, high, or weak.

Perfect positive or perfect negative correlations are when all the points of data fit on the line of best fit.

High positive or high negative correlations are when most of the points of data are clumped close to the line of best fit.

Weak positive or weak negative correlations are when the points of data are scattered but slightly resemble the line of best fit.

Scatter Plots

Scatter plots are graphs used to visually represent a correlation between two sets of data, or variables. Our graph will have the independent variable on the $x$-axis and the dependent variable on the $y$-axis.

Example 1: Positive Correlation

Let's say we want to find the effect of height on shoe size, so we take a survey of all of our male friends to find a correlation between height and shoe size.

We can plot all of these points onto a scatter plot to get a visualization. Height is going to go on the $x$-axis as it is our independent variable, and shoe size will be on the $y$-axis as it is our dependent variable.

We can see here that, in general, our taller friends have a bigger shoe size. This is called a positive correlation. This does not mean that our taller friends will always wear bigger shoes than our shorter ones. We can see this with the data point at $71$ inches. That corresponding shoe size is larger than the points at $72$ and $74$ inches.

Even if we didn't know the exact data behind the points shown on the graph, we can tell that this is a positive correlation because the $y$ values generally increase as $x$ goes up.

Example 2: Negative Correlation

A negative correlation will be the opposite. The $y$ values will generally decrease as $x$ goes up.

The general trend of this scatter plot is downward, even with some points out of place.

Example 3: No Correlation

A scatter plot with no correlation means that the $x$ value has little to no effect on the $y$ value.

The points in this scatter plot are in a cluster with no real trend up or down.

Correlation vs. Causation

Correlations are general trends shown in data, but trends in our data don't imply causation. Causation is one event that will always lead to another event. For instance, adding an acid to water will always lower the pH.

You can see that our original scatter plot shows a correlation, because a causation would mean that height exactly predicts shoe size. We couldn't have $4$ people at $70\text{ in}$ with different shoe sizes if it was a causation relationship.

(Video) Scatter Plot and Linear Correlation

by Diane Koenig

Diane Koenig has a video discussing different types of correlation in linear scatter plots.

$\large{\text{Summary}}$

Positive Correlation

Positive correlated plots have data that rise as you move left to right on the horizontal axis. This tells us that as one of the variables increases, the other variable also increases.

Note: This does not mean that one variable causes the other. It only tells us that there is a relationship or a trend.

Negative Correlation

Negative correlation plots have data that decreases as you move left to right. This tells us that as one of the variables increases, the other variable decreases.

No Correlation

No correlation plots have data that is all over the place. They have no discernable pattern on horizontal axis or vertical axis.

Perfect, Strong, and Weak

Scatter plots also can have an additional adjective to describe their correlation: perfect, strong, or weak.

• Perfect correlations fit on an exact (straight) line.
• Strong correlations fit closely to an exact line.
• Weak correlations fit loosely to an exact line.

(Video) Correlation vs. Causation: How Ice Cream Kills!

by Decision Skills

When it comes to analyzing sets of data, it is important to understand and recognize the difference between correlation and causation. This video from Decision Skills gives a humorous and informative explanation on the differences.

$\large{\text{Summary}}$

This video by Decision Skills shows that the amount of ice cream sold is positively correlated with obesity, higher crime rates, increase deaths by drowning, and increase forest fires.

This does not mean that buying more ice cream causes more people to get obese, more crimes to happen, more people drowning, and more forests catching on fire.

Correlation is when two things are related, but one does not cause the other. This could be because two things are related to a third factor but they could also just be coincidental.

One reasoning for the correlation between ice cream and forest fires, is weather. People by more ice cream when it's hot out, and more forest fires happen when it's hot out.

Causation is when you can claim one thing causes another to happen.

The pharmaceutical industry is a good example of this. In order for them to claim some medicine has the effect of lowering cholesterol, they have to test the drug. The FDA requires a special process be done.